Mutual Induction

Q. If a coil of $50$ turns area $5.0c{m}^2$ is suddenly removed from magnetic field. It is observed that charge of $5\times {10}^{-4}C$ flows into the coil. If the resistance of the coil is $100\Omega$, the magnetic flux density in $Wb/m^2$ is

1. $2$
2. $3$
3. Zero
4. $5$

Q.

What is the dimension formula of the potential gradient?

Q. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation $I=I_{0}sin\omega t$, where $I_0=10Aand\omega =100\pi radian/sec$. The maximum value of e.m.f. in the second coil is

1. $2\pi$
2. $5\pi$
3. $\pi$
4. $4\pi$

Q.

A solenoid has 2000 turns wound over a length of 0.30 metre. The area of its cross-section is . Around its central section, a coil of 300 turns is wound. If an initial current of 2 A in the solenoid is reversed in 0.25 sec, then the e.m.f. induced in the coil is

1. 48 mV
2. 6 X 10^-4 V
3. 4.8 X 10^-3 V
4. 6 X 10^-2 V

Q. What is the mutual inductance of a two-loop system as shown with centre separation l

1. 
2. 
3. 
4. 

Q. Calculate the inductance of an air core solenoid containing $300$ turns if the length of the solenoid is $25.0\text{cm}$ and its cross-sectional area is $4.00{\text{cm}}^2$.

1. $1.80\times {10}^{-4}\text{H}$
2. $1.81\times {10}^{-2}\text{H}$
3. $3.62\times {10}^{-4}\text{H}$
4. None of the above

Q. An electron moves on a straight line path $\text{XY}$ as shown in the figure. The $\text{abcd}$ is a loop adjacent to the path of electron. What will be the direction of induced current, if any, induced in the loop?

1. $\text{adcb}$
2. The current will reverse its direction as the electron goes past the loop
3. No current is induced
4. $\text{abcd}$

Q. in an L-C circuit consisting of 20 mH inductor and 0.1 microfarad capacitor, the maximum current in the circuit is 0.15 A. The maximum current in the circuit is 0.15 A. The maximum voltage across the capacitor is approximately : a-60 V b-67 V

Q.

The coils A and B having turns $300$and $600$respectively are placed near each other, on passing a current of $3.0$ampere on A, the flux linked with A is $1.2\times {10}^{-4}$ weber and with B it is $9.0\times {10}^{-5}$ weber. The mutual induction of the system is?

1. $2\times {10}^{-5}H$

2. $3\times {10}^{-5}H$

3. $4\times {10}^{-5}H$

4. $6\times {10}^{-5}H$

Q.

A hairpin-like shape as shown in the figure is made by bending a long current-carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the center of the semicircle?

1. $\begin{array}{l}\frac{{\mu }_{0}I}{4\pi r}(2-\pi )\end{array}$

2. $\begin{array}{l}\frac{{\mu }_{0}I}{4\pi r}(2+\pi )\end{array}$

3. $\begin{array}{l}\frac{{\mu }_{0}I}{2\pi r}(2+\pi )\end{array}$

4. $\begin{array}{l}\frac{{\mu }_{0}I}{2\pi r}(2-\pi )\end{array}$

Q. In a step up transformer the turn ratio is 1:2, A lechlanche cell of e.m.f. 1.5V is connected across primary. The voltage across the secondary is

1. 3 V
2. 0.75V
3. 75 V
4. Zero

Q. A light disc made of Aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis, as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)

1. Rotate in the direction opposite to the direction of magnet's motion
2. Rotate in the same direction as the direction of magnet's motion
3. Not rotate and its temperature will remain unchanged
4. Not rotate, but its temperature will slowly rise

Q.

Define mutual inductance between a pair of coils. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other.

Q. Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10{\text{cm}}^2$ and length $20\text{cm}$. It one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is

1. $4.8\pi \times {10}^{-4}\text{H}$
2. $2.4\pi \times {10}^{-4}\text{H}$
3. $4.8\pi \times {10}^{-5}\text{H}$
4. $2.4\pi \times {10}^{-5}\text{H}$

Q. The magnetic flux linked with a coil is given by the equation $\varphi =2t^2-8t+16$. what will be the magnitude of flux linked with the coil, when induced emf in the coil is zero?

1. $2\text{Wb}$
2. $4\text{Wb}$
3. $6\text{Wb}$
4. $8\text{Wb}$

Q.

How does the number of turns affect inductance?

Q.

State any two uses of eddy currents?

Q.

In an electric circuit, two resistors of 12 Ω each are joined in parallel to a 6 V battery. Find the current drawn from the battery.

Q. Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be maximum in -



Assume that the area of the smaller coil is very small.

1. $A$
2. $B$
3. $C$
4. The same in all situations

Q. An equilateral triangular loop having a resistance $R$ and length of each side $l$ is placed in a magnetic field which is varying at $\frac{dB}{dt}=1\text{T/s}$. The induced current in the loop will be

1. $\frac{\sqrt{3}}{4}\frac{l^2}{R}$
2. $\frac{4}{\sqrt{3}}\frac{l^2}{R}$
3. $\frac{\sqrt{3}}{4}\frac{R}{l^2}$
4. $\frac{4}{\sqrt{3}}\frac{R}{l^2}$

Q. A rod of length $l$ is rotating about one end $\text{A}$ in a uniform magnetic field $B$ which is perpendicular to the plane of rotation of the rod. Point $\text{B}$ is the midpoint of the rod. Find the potential difference between points $\text{B}$ and $\text{C}$ if the potential difference between $\text{A}$ and $\text{C}$ is $25\text{V}.$

1. $\frac{12}{5}\text{V}$
2. $\frac{25}{4}\text{V}$
3. $\frac{75}{4}\text{V}$
4. $\frac{7}{5}\text{V}$

Q. For what value of R in the circuit as shown in figure. Current
passing through 4 $\Omega$ resistance will be zero.

1. $1\Omega$
2. $2\Omega$
3. $3\Omega$
4. $4\Omega$

Q.

The mutual inductance between two coils is 1.25 henry. If the current in the primary coil changes at a rate of 80 ampere/second, then the induced e.m.f. in the secondary coil is

1. 12.5 V

2. 64.0 V

3. 0.016 V

4. 100.0 V

Q.

The correct relation between $\alpha$(ratio of collector current to emitter current) and $\beta$ (ratio of collector current to base current) of a transistor is

1. $\alpha =\frac{\beta }{1+\beta }$

2. $\alpha =\frac{\beta }{1-\alpha }$

3. $\beta =\frac{1}{1-\alpha }$

4. $\beta =\frac{\alpha }{1+\alpha }$

Q. A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to

1. $l/L$
2. $l^2/L$
3. $L/l$
4. $L^2/l$

Q. If $V_{AB}=4\text{V}$ in the given figure, then the value of internal resistance $x$ of battery having emf $2\text{V}$ will be

1. $5\Omega$
2. $10\Omega$
3. $15\Omega$
4. $20\Omega$

Q. A solenoid of $0.4\text{m}$ length with $500$ turns carries a current of $3\text{A}.$ A coil of $10$ turns and of radius $0.01\text{m}$ carries of $0.4\text{A}$. The torque required to hold the coil with its axis at right angle to that of the solenoid is :

1. $6{\pi }^2\times {10}^{-7}\text{Nm}$
2. $3{\pi }^2\times {10}^{-7}\text{Nm}$
3. $9{\pi }^2\times {10}^{-7}\text{Nm}$
4. $12{\pi }^2\times {10}^{-7}\text{Nm}$

Q.

If an electric current flows in a clockwise direction in a circular loop, facing towards you, which magnetic pole is observed by you?

Q.

How does the mutual inductance of a pair of coils change when distance between the coils is increased?

Q.

An air core solenoid has 1000 turns and is one metre long. Its cross – sectional area is $10c{m}^2$. Its self – inductance is

1. 2.56 mH

2. 1.92 mH

3. 1.26 mH

4. 2.78 mH